The mean of 20 numbers is 43.


The mean of 20 numbers is 43. If 6 is subtracted from each of the numbers, what will be the new mean?


Let the numbers be $x_{1}, x_{2}, \ldots x_{20}$.

We know:

Mean $=\frac{\text { Sum of observations }}{\text { Number of observations }}$

Thus, we have:

$43=\frac{x_{1}+x_{2}+\ldots \ldots+x_{20}}{20}$

$\Rightarrow 860=x_{1}+x_{2}+\ldots \ldots+x_{20} \ldots \ldots$ (i)

Numbers after subtraction: $\left(x_{1}-6\right),\left(x_{2}-6\right), \ldots\left(x_{20}-6\right)$

$\therefore$ New Mean $=\frac{\left(x_{1}-6\right)+\left(x_{2}-6\right)+\ldots \ldots . .+\left(x_{20}-6\right)}{20}$

$=\frac{\left(x_{1}+x_{2}+\ldots \ldots \ldots+x_{20}\right)-(20 \times 6)}{20}$

$=\frac{860-120}{20} \quad[$ From $(\mathrm{i})]$



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